Bad Beta, Good BetaJohn Campbell and Tuomo VuolteenahoHarvard University and NBER

Presentation atOxford Finance Summer Symposium11/6/2004

RESEARCH AGENDA

High P/B growth or glamour?High P/B must in the long run forecast either high profitability (ROE) or low stock returns (or both)If high P/B forecasts stock returns, this may be because high-P/B stocks are less risky or because they are overvalued (or both)If high-P/B stocks' returns are less risky than low-P/B stocks', is this risk differential caused by differential risk in fundamentals or in mispricing (or both)?

Growth or glamour?Does high P/B forecast high ROE or low returns?High ROE justifies high priceLow stock returnscaused by risk or mispricing?RiskValuation level caused by mispricingis risk caused by fundamentals or mispricing?Risks caused by covariances in mispricingRisk is caused by covariances in fundamentalsBBGB

BAD BETA, GOOD BETA

The CAPMPeople have short investment horizonsThe average investor holds the marketIf an asset has a high return when the market performs poorly, then the asset is insurancei.e., low or even negative market betaIf an asset performs poorly when the market performs poorly, then it is riskyi.e., high market betaThe average investor requires a high return to hold risky assets, and accepts a low return to hold insurance

Why does the market fall?Bad news about future cash flows:wealth decreases and future investment opportunities remain constantThe discount rate or cost of capital applied to the market's cash flows increaseswealth decreases but future investment opportunities improve

To a long-horizon investor (with a constant relative risk aversion higher than unity), the first case is much worse news than the secondSuppose market portfolio of only corporate bonds: Would you rather have bonds defaulting or interest rates going up?

Intuition from Gordon modelD is dividend, P is price, k is discount rate, and g is dividend growth

k (discount rate news) and/or g (cash-flow news) P

Merton's ICAPM ideaWe break the market return in two components:

We also break up the CAPM beta of a stock into two components: cash-flow beta, CFdiscount-rate beta, DR

Merton's ICAPM ideaIntuitively, covariance or beta with the really bad market moves (market's cash-flow news) should have a higher risk premium than covariance or beta with the less bad market moves (market's discount-rate news)Campbell's (1993) version of Merton's (1973) ICAPM predicts:discount-rate-beta premium should equal the variance of the market return, andcash-flow-beta premium should be times higher, where is the coefficient of relative risk aversion of a representative investorThis is because poor returns driven by increases in discount rates are partially compensated by improved prospects for future returns

Beta and cholesterolIt used to be thought that heart attack risk could be measured by the overall level of cholesterol. Routine blood tests reported this level.Now we know there are two types of cholesterol, HDL and LDL. One (bad cholesterol) strongly increases the risk of a heart attack, the other (good cholesterol) weakly reduces it. Routine blood tests now report the two levels separately.Similarly, beta has two types, but in this case good beta is really not so bad beta as it does increase the risk premium.We hope that routine risk analysis will in the future report both types of beta separately.

An illustration The Empire Strikes BackBad BetaNot so bad beta

Our paper's three stepsEstimate the market's cash-flow and discount-rate newsUsing the estimated series, measure the cash-flow and discount-rate betas for various assetsSee how these betas explain average returns, and compare the premia to those predicted by the theory

Summary of resultsValue and small stocks have higher bad cash-flow betas than growth and large stocks explains the value and size premiaGrowth stocks have negative CAPM alphas because their betas are predominantly of the good discount-rate variety explains the negative CAPM alphas of growth stocksSorting on past CAPM betas induces little spread in mean returns in the post-1963 sample, because the sort creates a spread only in the good discount-rate beta.

Risk vs. return 1963:7-2001:12E(Ri-Rrf) = var(rM)i,DR +var(rM)i,DR +eiVertical axis is the average realized returnHorizontal axis is the predicted average return's are selected ME-and-BE/ME-sorted portfolios's are beta-sorted portfolios

Some previous researchThe ICAPM theory: Merton (1973), Campbell (1993)Decomposing the market's return: Campbell and Shiller (1988a, 1988b), Campbell (1991), Campbell and Ammer (1993)Value spread predicts the market return: Eleswarapu and Reinganum (2001), Brennan, Xia, and Wang (2001)Value stocks are more sensitive than growth stocks to market's cash-flow news: Liew and Vassalou (2000), Cohen, Polk, and Vuolteenaho (2002)Cross-sectional tests of the ICAPM: Campbell (1996), Li (1997), Hodrick, Ng, and Sengmuller (1999), Lynch (1999), Chen (2000), Brennan, Xia, and Wang (2001), Ng (2002), Guo (2000), etc.

ESTIMATING NEWS

Paper's three empirical stepsEstimate the market's cash-flow and discount-rate newsUsing the estimated series, measure the cash-flow and discount-rate betas for various assetsSee how these betas explain average returns, and compare the premia to those predicted by the theory

Idea of news identificationIf an assets return is unexpectedly high, its expected cash flows must have increased (i.e., cash-flow news must have been positive), and/or future expected returns decreased (i.e., discount-rate news must have been negative) The objective is to empirically split the market return into these two componentsWe use the Campbell-Shiller log-linear present-value model and a VAR to do just that

Defining news termsCash-flow news: Change in discounted sum of current and future expected dividend growth ratesDiscount-rate news: Change in discounted sum of future expected returnsSet the discount coefficient to .95 annualized

VAR implementationAssume that a VAR model generates returnsOne can then compute unexpected returns and discount-rate newsCash-flow news can be taken as a residual

VAR state variablesExcess market return log return on CRSP VW minus log return on three-month T-billsTERM yield spread (in percentage points)Yield on ten-year taxable T-bonds minus yield on short-term taxable T-notesSmoothed P/E Log S&P 500 price index minus log 10-year trailing moving average of S&P 500's aggregate earningsSmall-stock value spreadLog(BE/ME) of small-value Fama-French 2-by-3 portfolio minus log(BE/ME) of small-growth portoflio

Logic behind state variablesTERM yield spread High TERM yield spread forecasts high returns on long-term bondsSince stocks are long-term assets, expected stock returns should also be highPredicted coefficient positive Smoothed P/E Ten-year trailing moving average controls for cash-flow-generating ability of the stocks in S&P 500Holding cash-flow-generating ability constant, higher price must mean lower future stock returnsPredicted coefficient negative

Logic behind state variablesSmall-stock value spreadIf the ICAPM is to explain the value effect, value minus growth stock returns must be correlated with changes in discount rates, so a moving average of these returns should be a proxy for the level of the discount rate Growth stocks have a longer "duration," thus their values should be especially dependent on discount ratesImperfect-capital-markets story: High discount rates = SEO market is closed. Maybe small growth stocks require financing simply to survive?Small growth stocks sensitive to "irrational exuberance?"All these phenomena likely to be more extreme for small stocksPredicted coefficient negative

VAR state-variable dataPEVSTY

Monthly VAR, 1928:12-2001:12

Properties of the news terms

Moving-average news

Summary of the market's newsAt monthly frequency, market's discount-rate news are about twice as volatile as cash-flow news (5% per month vs. 2.5% per month)Correlation between the news terms is low (.11)An interpretation of the VAR: Negative cash-flow news corresponds to a profit recessionPositive discount-rate news corresponds to a valuation recessionA drop in stock prices that is accompanied by a drop in the P/E, higher TERM yield spread, and a shrinking value spread are signs of a valuation recession

MEASURING BETAS

Paper's three empirical stepsEstimate the market's cash-flow and discount-rate newsUsing the estimated series, measure the cash-flow and discount-rate betas for various assetsSee how these betas explain average returns, and compare the premia to those predicted by the theory

Defining betasWe use fitted values of VAR news to estimate betas on various portfoliosThe denominator is equal to variance of unexpected market returnWe include a lag to alleviate infrequent-trading problems, sluggish reaction of small stocks to new information, etc.

Test assetsWe measure the cash-flow and discount-rate betas on Fama-French 25 ME-and-BE/ME-sorted portfoliosWe also create risk-sorted portfolios by sorting stocks on pre-estimated regression loadings on market return, change in term-yield spread, and change in the small-stock value spreadData ranges:Full period, 1929:1-2001:12Early subsample, 1929:1-1963:6Modern subsample, 1963:7-2001:12

Estimates for early period

Estimates for modern period

Beta evolutionSmall minus bigValue minus growthDRCF

PRICING TESTS

Paper's three empirical stepsEstimate the market's cash-flow and discount-rate newsUsing the estimated series, measure the cash-flow and discount-rate betas for various assetsSee how these betas explain average returns, and compare the premia to those predicted by the theory

Epstein-Zin objective functionWe assume that long-horizon investor has Epstein-Zin (1989, 1991) preferencesIf the elasticity of intertemporal substitution () approaches 1, the optimal consumption-wealth ratio approaches a constant (=1-)

Epstein-Zin risk premiaSuppose that the investor follows an optimal portfolio strategy, denoted by pCampbell (1993) shows that the approximate optimality of portfolio strategy p requires that the following first-order conditions are satisfied:

Substituting out consumptionDiscount-rate news NDR

Asset pricing modelRecognizing that unexpected return equals cash-flow news minus discount-rate news allows us to rewrite the first-order condition:Premium on cash-flow betaPremium on discount-rate beta

ImplementationSet the reference portfolio to the CRSP value-weight index portfolioUse an unconditional betas and mean returnsUse average simple returns on the left hand sideInclude a lag in beta estimationOne free parameterPlug in the market's historical variance

Test assets25 Fama-French ME-and-BE/ME-sorted portfoliosValue vs. growthSmall caps vs. large caps20 risk-sorted portfolios formed on betas w/r market return, change in term-yield spread, and change in the small-stock value spreadData ranges:Full period, 1929:1-2001:12Early subsample, 1929:1-1963:6Modern subsample, 1963:7-2001:12

Early-period pricing tests

Modern-period pricing test?!?

Post-1963, ICAPM beats CAPMR2 = 47.4%R2 = - 61.6%

Critical issuesThe following steps are critical for the empirical success of our model:Inclusion of the small-stock value-spread variable in the VAR state vectorInclusion of at least one lagged month at the beta-estimation stage = value between .941/12 and .961/12 Exclusion of momentum portfolios from the asset-pricing test

CONCLUSIONS

ConclusionsMerton's ICAPM predicts that, if investors are conservative, "bad" cash-flow beta (covariance of a firm's stock return with the market's cash-flow news) should have a high premium"good" discount-rate beta (covariance of a firm's stock return with the market's discount-rate news) should have a very small premium

ConclusionsWe find that this prediction is supported by the data:High returns of value and small stocks are explained by their high bad cash-flow betasGrowth stocks have negative CAPM alphas because their betas are predominantly of the good discount-rate varietyThe post-1963 sorts on CAPM beta only create a spread in the good discount-rate beta minimal premiumThe model works with only one degree of freedom (zero-beta rate constrained to T-bill rate and discount-rate-beta premium to market's variance.)

Open questionsWhere is this discount-rate variation coming from?What are the exact economic fundamentals that cause varying sensitivities to cash-flow and discount-rate news?Are high NDR betas of growth stocks due to covariance of growth stocks' cash flows or expected returns with the market's discount-rate news?Market timing investor's first-order conditionPricing of momentum portfolios

APPENDIX

Time-varying covariances

Premia on news covariancesPremium on covariance with -NDR, ICAPM predicts 1Premium on covariance with NCF, ICAPM predicts

Suppose we discount a dividend stream growing at a constant rate g at a constant discount rate k (or factor 1+k). Then, the present value is simply P = D/(k-g).